Cremona's table of elliptic curves

13552 = 2⁴ · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2- 7+ 11-	Signs for the Atkin-Lehner involutions
Class	13552s	Isogeny class
Conductor	13552	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	9390678757289984 = 212 · 76 · 117	Discriminant
Eigenvalues	2- -2 -2 7+ 11- -4 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-99744,11159476]	[a1,a2,a3,a4,a6]
Generators	[-204:4802:1]	Generators of the group modulo torsion
j	15124197817/1294139	j-invariant
L	1.9925628115896	L(r)(E,1)/r!
Ω	0.39974598064303	Real period
R	2.4922862368552	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	847c2 54208cf2 121968ed2 94864cs2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13552s2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-2	-2	+	-	-4	-4	0	4	6	-10	-6	-4	12	10	-6	-2	0	-8	12	8	8	0	-6	-10

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Quadratic twists for elliptic curve 13552s2

-4	8	-3	-7	-11
847c2	54208cf2	121968ed2	94864cs2	1232i2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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